Problem: $79$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $91$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Solution: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 79}$ ${x = 4y-91}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-91}$ for $x$ in the first equation. ${(4y-91)}{+ y = 79}$ Simplify and solve for $y$ $ 4y-91 + y = 79 $ $ 5y-91 = 79 $ $ 5y = 170 $ $ y = \dfrac{170}{5} $ ${y = 34}$ Now that you know ${y = 34}$ , plug it back into ${x = 4y-91}$ to find $x$ ${x = 4}{(34)}{ - 91}$ $x = 136 - 91$ ${x = 45}$ You can also plug ${y = 34}$ into ${x+y = 79}$ and get the same answer for $x$ ${x + }{(34)}{= 79}$ ${x = 45}$ There were $45$ home team fans and $34$ away team fans.